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Derivatives

Derivatives

Slope of a Line Between Two Points on a Function Exercises

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, what is the slope of the secant line between the points (a, f(a)) and (bf(b))?

f(x) = x– 2, a = -2, b = 2.

Example 6

Given the values of a and b, what must h be so that a + h = b?

a = 4, b = 4.25.

Example 7

Given the values of a and b, what must h be so that a + h = b?

a = -1, b = -1.5.

Example 8

For the given function f, value of a, and value of h, what is 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, what's 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, what's 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, what's 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, what's the slope of the secant line between (af(a)) and (a hf(a + h))?

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