  For which value(s) of x does f(x)=8x3/3 +5x2 −10x+15 have a tangent line of slope −7? If there is more than one answer, give all of the x-values separated by commas, e.g. if f(x) has a tangent line of slope −7 at x=3 and x=5 enter 3,5.

Question

For which value(s) of x does f(x)=8x3/3 +5x2 −10x+15 have a tangent line of slope −7? If there is more than one answer, give all of the x-values separated by commas, e.g. if f(x) has a tangent line of slope −7 at x=3 and x=5 enter 3,5.

Step 1

We have been given a function and we need to figure out the x coordinates of the points where tangent lines have a slope equal to -7.

Step 2

We know that slope of a tangent line is equivalent to derivative of the function. Therefore, we will find the derivative of the given function and will set it equal to -7 and finally, we will solve for x.

Let us first find the derivative of the given function using power rule of derivatives as shown below:

Step 3

Upon setting this derivative equal to -7, we get a quadratic equation and...

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