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Allisa [31]
3 years ago
10

A tangent to the curve y=6x-x² cuts the x axis at point P. Find the coordinates of P. Help me calc the coordinates please​

Mathematics
1 answer:
Ilya [14]3 years ago
6 0

We know that the line is tangent at the point (2,8)

The derivative of the function at x=2 is

f'(x) = 6-2x \implies f'(2) = 6-4=2

So, the tangent line passes through the point (2,8) and has slope 2. The equation is

y-8 = 2(x-2) \iff y = 2x+4

This line crosses the x axis where y=0:

0 = 2x+4 \iff 2x = -4 \iff x = -2

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