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

a)
`(dy)/(dx) = -27`, b)
`m = -27`

Explanation:

a) The instantaneous rate of change is:

`(dy)/(dx) = 8\cdot x + 5`

`(dy)/(dx) = 8\cdot (-4)+5`

`(dy)/(dx) = -27`

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

`m = -27`