# Slope of a tangent line and derivatives

Find the point on the graph of the given function at which the slope of the tangent line is the given slope.

f(x)= (x^3) + (9x^2) + 36x +10

slope of the tangent line = 9

What is the ordered pair?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Find the point on the graph of the given function at which the slope of the tangent line is the given slope.

slope of the tangent line = 9

What is the ordered pair?

Slope of the tangent line is given by the derivative of the function. So, the slope of the tangent line for the curve is given by . It is given that the tangent line has given slope =9. Hence we should have

This gives . So, at the value of x=-3, the curve will have a tangent whose slope is 9. Plugging the value of x=-3 in f(x) ie., finding f(-3), we get

Hence the y-coordinate of the point at which the tangent line has the slope equal to 9 is -44. Hence the ordered pair is (-3, -44)

https://brainmass.com/math/derivatives/slope-tangent-line-derivatives-297510