* Site-Outage Notice: Our engineering elves will be tweaking the Shmoop site from Monday, December 22 10:00 PM PST to Tuesday, December 23 5:00 AM PST. The site will be unavailable during this time.
Dismiss
© 2014 Shmoop University, Inc. All rights reserved.
Derivatives

Derivatives

Example 1

For the given function f and values of a and b, find the slope of the secant line between the points (af(a)) and (bf(b)): 

f(x) = x2a = 1, b = 2.

Example 2

For the given function f and values of a and b, find the slope of the secant line between the points (a, f(a)) and (b, f(b)):

f(x) = x2a = 1, b = 1.5.

Example 3

For the given function f and values of a and b, find the slope of the secant line between the points (a, f(a)) and (bf(b)):

f(x) = sin(x), a = 0, b = π/2.

Example 4

For the given function f and values of a and b, find the slope of the secant line between the points (a, f(a)) and (bf(b)):

f(x) = x3 - 2x + 3, a = 1, b = 4.

Example 5

For the given function f and values of a and b, find the slope of the secant line between the points (a, f(a)) and (bf(b)):

f(x) = x4 - 2, a = -2b = 2.

Example 6

Given the values of a and b, find h so that a + h = ba = 4, b = 4.25.

Example 7

Given the values of a and b, find h so that a + h = ba = -1, b = -1.5.

Example 8

For the given function f, value of a, and value of h, find the slope of the secant line between (af(a)) and (a + hf(ah)):

f(x) = x2, a = 1, h = 0.1.

Example 9

For the given function f, value of a, and value of h, find the slope of the secant line between (af(a)) and (a + hf(a + h)):

f(x) = 1 - x2, a = 0, h = 0.1.

Example 10

For the given function f, value of a, and value of h, find the slope of the secant line between (af(a)) and (a + hf(a + h)):

f(x) = cos(x), a = 0, h = -π/2.

Example 11

For the given function f, value of a, and value of h, find the slope of the secant line between (af(a)) and (a + hf(a + h)):

f(x) = x3x, a = 1, h = 4.

Example 12

For the given function f, value of a, and value of h, find the slope of the secant line between (af(a)) and (a + hf(a + h)):

f(x) = 3x, a = -2, h = -0.2.

Advertisement
Noodle's College Search
Advertisement
Advertisement
Advertisement