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

Question

Let f(x)= 6x⁴+2

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

what is the slope at x=4?

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

the tangeant line y=?

 

Answer 1

1) The limit equation to find the slope will look like this: f'(x) = lim_x→4[[f(x+4)-f(x)]÷4]. To find the slope at x=4 just plug 4 in the resulting equation.

 

2) The tangent line equation will look like this: y = f(4) + f'(4)(x-4)

 

I hope this helps.