If f′(−2) = 7, find an equation of the line tangent to the graph of f at the point (−2,4).

Use the definition of the derivative to evaluate the following limits.

${\lim }_{x\to 2}{\frac{5^x-25}{x-2}}_{}$

An equation of the line tangent to the graph of f at the point (2,7) is y = 4x−1. Find f(2) and f′(2).

An equation of the line tangent to the graph of g at x = 3 is y = 5x + 4. Find g(3) and g′(3).

If h(1) = 2 and h′(1) = 3, find an equation of the line tangent to the graph of h at x = 1.

A projectile is fired vertically upward into the air; its position (in feet) above the ground after t seconds is given by the function s (t). For the following functions, use limits to determine the instantaneous velocity of the projectile at t = a seconds for the given value of a.

s(t) = -16t² + 128t + 192; a = 2

Use definition (1) (p. 133) to find the slope of the line tangent to the graph of f at P.

f(x) = x² - 5; P(3,4)

Use definition (1) (p. 133) to find the slope of the line tangent to the graph of f at P.

f(x) = -3x² - 5x + 1; P(1,-7)

Use definition (1) (p. 133) to find the slope of the line tangent to the graph of f at P.

f(x) = 1/x; P(-1,-1)