Question

g and Consider the following. f(x) = 4x2 + 5x − 18 (a) Find the instantaneous rate of change of the function at the value x = −4. f '(−4) = (b) Find the slope of the tangent at the value x = −4.

Answer 1

Answer:

a) $\frac{dy}{dx} = -27$, b) $m = -27$

Step-by-step explanation:

a) The instantaneous rate of change is:

$\frac{dy}{dx} = 8\cdot x + 5$

$\frac{dy}{dx} = 8\cdot (-4)+5$

$\frac{dy}{dx} = -27$

b) The slope of the tangent line is equal to the instantaneous rate of change found previously.

$m = -27$