SOLUTION: 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 answers completely.)
f(x) = 4x^2 + 3x
Step 1
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Question 1160763: 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 answers completely.)
f(x) = 4x^2 + 3x
Step 1: f(x + h)=
Step 2: f(x + h) − f(x)=
Step 3: f(x + h) − f(x)/h=
Step 4: f '(x) = lim h→0 f(x + h) − f(x)/h=
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's find f(x+h)
Replace every x with (x+h)
FOIL rule
Distribute. This is one way to write the result for step 1.
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Now subtract off f(x)
This is the result for step 2.
Notice how each term has an 'h' in it
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That common h will be factored out to help cancel and simplify things as shown below
The result for step 3.
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As h approaches infinity, the expression will approach . All I did here was plug in h = 0. Afterward, you simplify to go from to
Therefore, if f(x) = 4x^2+3x, then f'(x) = 8x+3 is the derivative.
Side note: To find the slope of the tangent line at any given point (x,y), you would plug the x coordinate into f'(x) = 8x+3 and simplify.
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