Use the limit process to find the slope of the line tangent to the graph

Question

Let f(x)- 6x⁴+2

 

A) Use the limit process to find the slope of the line tangent to the graph of f at x=4

the slope at x=4 is?

 

B) Find an equation to the line tangent to the graph of f at x=4

tangent line: y=

 

Answer 1

Daila,

 

       I'll get you started, slope =df/dx=lim_h→0 {(f(x+h)-f(x))/h} and f(x)=6x⁴+2

 

now f(x+h)-f(x)=(6*(x+h)⁴ +2) - (6x⁴+2))=  6*(h⁴+4h³+6h²x²+4hx³+x⁴)-6x⁴  so now you take it combine like terms, notice the 6x⁴ terms cancel. Then divide this polynomial by h and take the limit as h goes to zero.

 

You should get 24x³ this is the slope of the tangent line at x. To find it at x=4 sub x=4 .

 

Try it

 

Jim