Question

Find the equation of the line tangent to $y = e^{4x}$ at $x = \frac{1}{4} \ln 5$. The equation of the line tangent is $y = $ 

          Find the equation of the line tangent to $y = e^{4x}$ at $x = \frac{1}{4} \ln 5$.
The equation of the line tangent is $y = $
Find the equation of the line tangent to y = e^4x at x = (1)/(4)ln 5. The equation of the line tangent is y =

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the equation of the line tangent to y=e^(4x) at x=(1)/(4)ln5. The equation of the line tangent is y= 1 Find the equation of the line tangent to y=e4x at x= In5. < The eguation of the line tangent is y=
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Transcript

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00:01 So we have our questions equation with us which is 4 y cubed plus x y minus y is equals to 256 x x -res to the power 4 and we need to find the equation of that tangent line at x equals to 1 so we'll find y first so y cube plus y minus y is equals to 256 this gets cancelled we get 4 y cube is equals to 256 divided by 4 which is 64 and we get the value of y as cube root of 64 which is 4 so we have x as 1 and we have y as 4 so we have the coordinates with us now we need to find d y by t x so for that we'll use implicit differentiation which which becomes 12 y squared into dy by d x plus x times y becomes y plus x d y plus x d y by d x minus d y by d x is equal to 256 multiplied by 4 becomes 1 024 x cubed now we'll key in 1 and 4 and find d y by d x so…
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