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ser-zykov [4K]
3 years ago
5

The tangent line to y= f(x) at (4,-6) passes through the point (10,9) Compute the following, f(4) and f'(4)

Mathematics
1 answer:
Anni [7]3 years ago
3 0
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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