How do you find the equation of tangent line to the curve # f(x) = 9tanx# at the point #(pi/4, f(pi/4)) #?

Answer 1

#36x-2y+18-9pi=0#

We have to find equation of tangent to curve #f(x)=9tanx# at point #(pi/4,f(pi/4))# i.e. #(pi/4,9tan(pi/4))# and as #tan(pi/4)=1#, this point is #(pi/4,9)#.
The slope of tangent is given by value of first derivative of #f(x)#, at that point I.e. at #(pi/4,9)#.
As #(df)/(dx)=9sec^2x# we have #f'(pi/4)=9sec^2(pi/4)=9xx(sqrt2)^2=18#
As slope is #18# and tangent passes through #(pi/4,9)#, its equation is
#(y-9)=18(x-pi/4)# i.e. #36x-2y+18-9pi=0#.

graph{(36x-2y+18-9pi)(y-9tanx)=0 [-4, 4, -20, 20]}

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Answer 2

To find the equation of the tangent line to the curve f(x) = 9tanx at the point (pi/4, f(pi/4)), we need to find the derivative of f(x) and evaluate it at x = pi/4. The derivative of f(x) = 9tanx is f'(x) = 9sec^2x. Evaluating f'(x) at x = pi/4, we get f'(pi/4) = 9sec^2(pi/4) = 9(2^2) = 36. Therefore, the slope of the tangent line is 36. Using the point-slope form of a line, the equation of the tangent line is y - f(pi/4) = 36(x - pi/4).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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