Bob asked in Science & MathematicsMathematics · 2 months ago

Calc question?

Let f(x)= 49-x^2

The slope of the tangent line to the graph of f(x) at the point (-7,0) is:

The equation of the tangent line to the graph of f(x) at (7,0) isy=mx+b for 

M =

and 

B=

2 Answers

Relevance
  • 2 months ago

    I answered a question very similar to this yesterday, but it seems to have been deleted. Also, you have (-7,0) at one place and then (7,0) at the other. I'll show you the method for the first point, but you can easily switch to x=7 to find the slope (m) and y-intercept (b) for the tangent line at the other point.

    STEP 1 - Calculate the first derivative.

    f'(x) = -2x

    STEP 2 - Use that to find the slope at x=-7:

    f'(-7) = -2(-7) = 14

    m = 14

    STEP 3 - Write the equation with the slope included.

    y = 14x + b

    STEP 4 - Plug in the point (-7,0)

    0 = 14(-7) + b

    0 = -98 + b

    b = 98

    Answer:

    y = 14x + 98

    Check the graph of the function and the tangent line in the link below.

  • 2 months ago

    f'(x) = -2x,

    so M at (-7,0) is 14.

    The equation is y = 14x + B,

    and the fact that (-7,0) is on the line shows that

    B = 0 + 14(7) = 98.

Still have questions? Get answers by asking now.