Best solutions to - "What is the equation of the line tangent..."

assumingsun

Answered question

2022-02-12

What is the equation of the line tangent to the curve

y = {(x^{2} - 35)}^{7}

at x=6?

Bleadafat9om

Beginner2022-02-13Added 13 answers

The tangent line in a point to a function, knowing its ascissa is:

y - f (x_{0}) = f^{'} (x_{0}) (x - x_{0}) .

So:

f (x_{0}) = f (6) = {(36 - 35)}^{7} = 1

and

f^{'} (x) = 7 {(x^{2} - 36)}^{6} \cdot 2 x \Rightarrow

f^{'} (6) = 7 {(36 - 35)}^{6} \cdot 2 \cdot 6 = 7 \cdot 1 \cdot 12 = 84 .

The tangent line is:

y - 1 = 84 (x - 6) \Rightarrow y = 84 x - 503 .

Heidy Prince

Beginner2022-02-14Added 15 answers

y = {(x^{2} - 35)}^{7}

If x=6 y=1
Derivative

y^{'} = 7 {(x^{2} - 35)}^{6} \cdot 2 x

Evaluate y'm

x = 6 \to y^{'} (6) = 7 {(36 - 35)}^{6} \cdot 2 \cdot 6 =

=7*12=84
m=84 is the slope of the tangent in

x_{0} = 6 y_{0} = 1

y - y_{0} = m (x - x_{0})

y-1=84(x-6)
y=84x-503

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