What is the tangent of f(x)=-x^2-x+3,\at x=-3 ?

The tangent of f(x)=-x^2-x+3,\at x=-3 is y=5x+12

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tangent of f(x)=-x^2-x+3,\at x=-3

tangent of

f (x) = - x^{2} - x + 3, at x = - 3

y = 5 x + 12

Solution steps

Find the tangent point:

(- 3, - 3)

Find the slope of

f (x) = - x^{2} - x + 3 : \frac{df ( x )}{d x} = - 2 x - 1

Compute the slope of

f (x) = - x^{2} - x + 3

x = - 3 : m = 5

Find the line with slope m=

5

and passing through

(- 3, - 3) : y = 5 x + 12

y = 5 x + 12

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What is the tangent of f(x)=-x^2-x+3,\at x=-3 ?
The tangent of f(x)=-x^2-x+3,\at x=-3 is y=5x+12