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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.

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xero099

Answer:

a) [tex]\frac{dy}{dx} = -27[/tex], b) [tex]m = -27[/tex]

Step-by-step explanation:

a) The instantaneous rate of change is:

[tex]\frac{dy}{dx} = 8\cdot x + 5[/tex]

[tex]\frac{dy}{dx} = 8\cdot (-4)+5[/tex]

[tex]\frac{dy}{dx} = -27[/tex]

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

[tex]m = -27[/tex]

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