Use the four step process to find the slope of the tangent line to the graph of the given function at any point. ( simplify your answer is completely)
f(x)= 8x^2 +3x
i’ve been trying to do this problem for 20 minutes,

Here, we are required to find the slope of the tangent line to the graph of the given function at any point.

The correct answer is 16x + 3.

The four step process to find the slope of the tangent line to the graph at any point is as follows;

First step (1):

f(x +h) = 8(x + h)² + 3( x + h) and yields;

f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

and, f (x + h) = 8x² + 16xh + 8h² + 3x + 3h.

Second step(2):

F(x+h) - f(x) = 8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

and, F(x+h) - f(x) = 16xh + 8h² + 3 h

Third step (3):

{F(x+h) - f(x)} / h = (16xh)/h + (8h²)/h + (3 h)/h

This in turn yields;

{F(x+h) - f(x)} / h = 16x + 8h + 3.

Fourth step(4):

lim f(x + h) - f(x)/ h =

h=>0

lim 16x + 8h + 3 = lim 16x + 8(0) + 3 = 16x + 3

h=>0. h=>0

Therefore, the slope of the tangent line to the graph of the given function at any point is;

16x + 3.

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The answer to your question is: 16x + 3

Step-by-step explanation:

Step 1 :      f(x) = 8x² + 3x

                f(x +h) =  8(x + h)² + 3( x + h)

                f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

                f (x + h) = 8x² + 16xh + 8h² + 3x + 3h

Step 2 f(x+h) - f(x) =  8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

                              = 8x² + 16xh + 8h² + 3x + 3h - 8x² -3x

                              = 16xh + 8h² + 3 h

Step 3 f(x + h) - f(x)/ h = h(16x + 8h + 3) /h

                                    = 16x + 8h + 3

Step 4 lim  f(x + h) - f(x)/ h = lim 16x + 8h + 3  = lim 16x + 8(0) + 3 = 16x + 3

        h ⇒0                           h ⇒0                     h ⇒0

3432532

step-by-step explanation:

the correct answer is x/3+10≥32

hope this !