Introduction for calculus derivative problems exam:
Two mathematicians, Namely Gottfried Leibniz and Isaac Newton, developed calculus. Calculus problems can be dividing into two branches: Differential Calculus problems and Integral Calculus problems. Differential calculus is use to measure the rate of change of a given quantity whereas the integral calculus is use to measure the quantity when the rate of change is known. The output of a function will change when we change the input value of a function. The measure of the change in the function is called as Calculus Derivatives.
Calculus derivative example problems:
The following solving problems are based on the derivatives.
Ex 1:
Determine the derivative dy/dx of the inverse of function f defined by
f(x) = (1/8) x - 2
Sol:
The first is used to find the inverse of f and differentiate it. To find the inverse of f we first write it as an equation
y = (1/8) x - 2
Solve for x.
x = 8y + 16.
Change y to x and x to y.
y = 8x + 16.
The above gives the inverse function of f. Let us find the derivative
dy / dx = 8
Ex 2:
Determine the critical number(s) of the polynomial function f given by
f(x) = x 4 - 108x + 100
Sol:
The domain of f is the set of all real numbers. The first derivative f ' is given by
f '(x) = 4 x^ 3 - 108
f '(x) is defined for all real numbers. Let us now solve f '(x) = 0
4 x^ 3 - 108 = 0
Add 108 on both sides,
4x^ 3– 108 108=108
4x^ 3= 108
x^ 3 = 27
x = 3 or x = -3
Since x = 3 and x = -3 are in the domain of f they are both critical numbers. Is this topic Limits of a Function in Calculus hard for you? Watch out for my coming posts.
Calculus derivative Practice Problems exam:
1) Determine the derivative dy/dx of the inverse of function f defined by
f(x) = x/2+ 3x/2 – 2
Answer: dy / dx = 2
2) Determine the critical number(s) of the polynomial function f given by
f(x) = x^ 3 - 48x + 10
Answer: X = 4 or X= -4
Two mathematicians, Namely Gottfried Leibniz and Isaac Newton, developed calculus. Calculus problems can be dividing into two branches: Differential Calculus problems and Integral Calculus problems. Differential calculus is use to measure the rate of change of a given quantity whereas the integral calculus is use to measure the quantity when the rate of change is known. The output of a function will change when we change the input value of a function. The measure of the change in the function is called as Calculus Derivatives.
Calculus derivative example problems:
The following solving problems are based on the derivatives.
Ex 1:
Determine the derivative dy/dx of the inverse of function f defined by
f(x) = (1/8) x - 2
Sol:
The first is used to find the inverse of f and differentiate it. To find the inverse of f we first write it as an equation
y = (1/8) x - 2
Solve for x.
x = 8y + 16.
Change y to x and x to y.
y = 8x + 16.
The above gives the inverse function of f. Let us find the derivative
dy / dx = 8
Ex 2:
Determine the critical number(s) of the polynomial function f given by
f(x) = x 4 - 108x + 100
Sol:
The domain of f is the set of all real numbers. The first derivative f ' is given by
f '(x) = 4 x^ 3 - 108
f '(x) is defined for all real numbers. Let us now solve f '(x) = 0
4 x^ 3 - 108 = 0
Add 108 on both sides,
4x^ 3– 108 108=108
4x^ 3= 108
x^ 3 = 27
x = 3 or x = -3
Since x = 3 and x = -3 are in the domain of f they are both critical numbers. Is this topic Limits of a Function in Calculus hard for you? Watch out for my coming posts.
Calculus derivative Practice Problems exam:
1) Determine the derivative dy/dx of the inverse of function f defined by
f(x) = x/2+ 3x/2 – 2
Answer: dy / dx = 2
2) Determine the critical number(s) of the polynomial function f given by
f(x) = x^ 3 - 48x + 10
Answer: X = 4 or X= -4
