Name: __________________________________________
Calculus Derivative Practice
1) Determine the equation of the derivative for each function below and express your
answer entirely in terms of positive exponents.
f ( x)  3 x  2
g ( x)   x3
h( x)  2 x 1
p( x)  x
r ( x)  6 x 4  5 x 2
3
s ( x)  7  x
t ( x) 
5
2
5
 x3
x2
v( x)  13.2
2) Find when
3)
dy
= 0, for y  1 x3  4 x 2  12 x .
3
dx
f ( x)  2 x 3 find f '(1)
4) f ( x)  x n determine the derivative of f(x) with respect to x.
5) If f  x   3g  x   2h( x) , find the equation for f '  x  in terms of g , h, g  and h '
 x3  1, x  1

6) Let f  x    2 , x  1 .
 x  4, x  1

a) Is f continuous at x = 1.
b) Determine the value of the left-hand derivative of f(x) and x=1
c) Determine the value of the right-hand derivative of f(x) and x=1
d) Is f differentiable at x = 1
7) Consider the curve y  x 4  4 x3  10 x 2  20 x .
3
Find the x-coordinates of any points where the tangent line to the curve is horizontal.
8) Determine the equation of the line tangent to the graph y   x3  4 x at x = 2.
9) Determine the equation of the line normal the graph y   x3  4 x at x = 2.
10) f ( x)  2 x 4  5 x 2 Determine f ‘(x) and f ‘’(x).
11) Given f(x) graph f ’(x)
3
f(x)
2
1
-6
-4
-2
2
4
6
-1
-2
-3
f ’(x)
3
2
1
-6
-4
-2
2
4
6
-1
-2
-3
12) Determine the x values when
d2y
 0 , if y  x 4  24 x 2
dx 2
13) g ( x)  3x 2  5 x and g '(a )  11 . Determine the value of a.
14) Graph a function with the following characteristics
a) f ‘ (2) = 0
b) f (x) is differentiable over the real numbers
c) f ‘ (x) > 0 when x > 2
3
2
1
-6
-4
-2
2
4
6
-1
-2
-3
15)Graph a function with the following characteristics
a) f(x) is continuous at x = 2
b) f(x) is not differentiable at x =2
c) f(x) is neither continous or differentiable at x = -3
3
2
1
-6
-4
-2
2
-1
-2
-3
4
6