Consider the graph of f(x)= 24 - x^2. Find the coordinates of the point P in the graph at which the tangent line passes through (7,0).

Question

Give your answer as a point's coordinates in the form ( * , * )

Thanks in advance

Answer 1

two points P are (2,20) and (12,-120)

the tangent line to the graph through either point also goes through (7,0)

-2x^2 + 14x = 24 - x^2

x^2 -14x + 24 =0

(x-12)(x-2) =0

x = 12 or 2

y = -120, 20

P(2,20) or P(12,-120)

Answer 2

[(24-x²)-0]/(x-7) = -2x

This equation says the slope of the tangent line equals the derivative.

24-x² = -2x² + 14x

x² - 14x + 24 =0

(x-12)(x-2)=0

The ordinates can be found by evaluating f(x) at x=2 and x=12