Given f(x)=2x^3−2, use a table to estimate the slope of the tangent line to f at the point P(−3,−56).

Question

1. Find the slope of the secant line PQ for each point Q(x,f(x)) with the x values given in the table. (Round each answer to 6 decimal places if necessary.)
2. Use the answers from the table to estimate the value of the slope of the tangent line at the point P. (Round your answer to the nearest integer.)

Answer 1

Hi Tylar E.,

Oh, for goodness sake, quit paying attention to the dribblings of math from your textbook and just calculate the slope directly from the function:

f(x) = 2x^3 - 2 . For y = ax^n the first derivative is: y ' = a*n*x^(n-1), so:

f '(x) = 2*3*x^2 ; at x=-3 this evaluates to 2*3*9 = 54

That's what your textbook is heading towards, anyway. The sooner you are there, the better!

--Cheers, -Mr. d.