1) Use the four-step process to find the slope of the tangent line to the graph

Question

1) 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.)

2) Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

3) Find the slope of the tangent line to the graph of the function at the given point.

f(x) = 4x + 3 at (1, 7)

m =  

Determine an equation of the tangent line.

3) The graph of a function is shown.

(a) Does f(x) have a limit at x = a, as x approaches a?

YesNo    

(b) Is f(x) continuous at x = a?

YesNo    

(c) Is f(x) differentiable at x = a?

YesNo   

5) The graph of a function is shown.

(a) Does f(x) have a limit at x = a, as x approaches a?

YesNo    

(b) Is f(x) continuous at x = a?

YesNo    

(c) Is f(x) differentiable at x = a?

YesNo   

Explanation / Answer

1) f(x) = -1

   Step 1:   f(x + h) = -1

    Step 2: f(x+h) – f(x) = -1 + 1 = 0

    Step 3: [f(x+h) – f(x)]/h = 0

    Step 4: f’(x) = 0

2) f(x) = -7x^2 + 9x

   Step 1:   f(x + h) = -7(x+h)^2 + 9(x+h) = -7x^2 – 7h^2 – 14xh + 9x + 9h

    Step 2: f(x+h) – f(x) = – 7h^2 – 14xh + 9h

    Step 3: [f(x+h) – f(x)]/h = – 7h – 14x + 9

    Step 4: f’(x) = -14x + 9

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