The tangent line to y= f(x) at (4,-6) passes through the point (10,9) Compute the following, f(4) and f'(4)
1 answer:
The solution to your problem is as follows:
The tangent line passes through (4,-6), so x = 4 when y = -6
=> f(4) = -6
The tangent line will have a constant gradient.
gradient is m = (-6 - 9)/(4 - 10) => 5/2
Equation is y - 9 = (5/2)(x - 10)
=> y - 9 = (5/2)(x-10)
<span>i.e. y = (5/2)(x-10) + 9
</span> y = (5/2)x - 25 + 9 = y = (5/2)x - 16
Now, f '(x) = dy/dx = 5/2
so, f '(4) = 5/2....i.e. gradient is 5/2 whatever the value of x.
I hope my answer has come to your help. Thank you for posting your question here in Brainly.
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