A tangent line and its normal line have a point of tangency to the function f(x) at (x, y). If the slop of the normal line is m=(8/7), what are the coordinates of the point of tangency? Please help, step by step explanation would be great

or approximately (0.544, 4.179)

Step-by-step explanation:

A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):

Set equal to 8/7 and solve for x:

Therefore, will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into to get the y-coordinate:

⇒ (49/900, 3761/900) or approximately (0.544, 4.179)

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step-by-step explanation:

x=6 and x=3

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