Prepare For Calculus Tests Exam
Introduction
Calculus is a measure of how a given function changes as it’s input change. Calculus mainly deals with the differentiation of functions with one or more variables. Calculus was two mathematicians, Namely Gottfried Leibniz and Isaac Newton. Calculus can be divided into Differential Calculus and Integral Calculus. Differential calculus is used to find the rate of change of a quantity; integral calculus is used to find the quantity where the rate of change is known. “Functions” are defined by a formula. The following problem helps to prepare for calculus exam.The test questions are discussed below.
Prepare Calculus Test Problems for exam:
The test questions are solved with detailed solutions for exam.
Example 1:
Determine the derivative dy/dx of the inverse of function f defined by
f(x) = x/2+ 3x/2 – 2
Solution:
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 = x/2+ 3x/2 – 2
y = 2x-2
Solve for x.
x = 2y + 2.
Change y to x and x to y.
y = 2x + 2.
The above gives the inverse function of f. Let us find the derivative
dy / dx = 2
Example 2:
Determine the critical number(s) of the polynomial function f given by
f(x) = x 4 – 108x + 100
Solution:
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.
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Prepare Practice Problems for calculus exam:
The test questions for exam are given below to workout. Prepare this questions for exam.
1) Determine the derivative dy/dx of the inverse of function f defined by
f(x) = x/4+ 3x/4 – 2
2) Determine the critical number(s) of the polynomial function f given by
f(x) = x 2 – 50x + 75
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