SOLUTION: Let f (x) = {{{ x^3 + 11 }}} and a = {{{ 3 }}} Find and simplify the quotient: {{{ (f(x)-f(a))/(x - a) }}} = Then find the slope {{{ M[a] }}} of the line tangent to th

Algebra ->  Equations -> SOLUTION: Let f (x) = {{{ x^3 + 11 }}} and a = {{{ 3 }}} Find and simplify the quotient: {{{ (f(x)-f(a))/(x - a) }}} = Then find the slope {{{ M[a] }}} of the line tangent to th      Log On


   

Question 987884: Let f (x) = +x%5E3+%2B+11+ and a = +3+
Find and simplify the quotient:
+%28f%28x%29-f%28a%29%29%2F%28x+-+a%29+ =

Then find the slope +M%5Ba%5D+ of the line tangent to the graph of f at the point (a, f (a)).
+M%5Ba%5D+ =

Please explain
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Let f (x) = +x%5E3+%2B+11+ and a = +3+
Find and simplify the quotient:
+%28f%28x%29-f%28a%29%29%2F%28x+-+a%29+
==============================
%28f%28x%29-f%28a%29%29%2F%28x+-+a%29+=+%28x%5E3+%2B+11+-+%28a%5E3%2B11%29%29%2F%28x-a%29
= %28x%5E3+-+a%5E3%29%2F%28x-a%29+=+%28x%5E2+%2B+ax+%2B+a%5E2%29
-----------
@ x = 3:
= %28x%5E3+-+27%29%2F%28x-3%29
= x%5E2+%2B+3x+%2B+9
=======================================
Then find the slope +M%5Ba%5D+ of the line tangent to the graph of f at the point (a,f(a))
f'(x) = 3x^2
f'(3) = 27