Solved: "What is the equation of the line tangent..."

Jazmin Strong

Answered question

2022-04-07

What is the equation of the line tangent to

f (x) = x^{2} \cos^{2} (x)

x = \frac{π}{4}

Answer & Explanation

firenzesunzc65

Beginner2022-04-08Added 16 answers

Explanation:
The equation of tangent line is given by
$(1) (y - y_{0}) = f^{'} (x_{0}) (x - x_{0})$ where $x_{0} = \frac{π}{4}$ and $y_{0} = f (x_{0})$ and $f^{'} (x_{0})$ is the value of derivative of f in $x_{0}$
Proceed:
$x_{0} = \frac{π}{4}$
$f (\frac{π}{4}) = \frac{π^{2}}{16} \cos^{2} (\frac{π}{4}) = \frac{π^{2}}{32} = y_{0}$
$f^{'} (x) = 2 x \cos^{2} x - 2 x^{2} \cos x \sin x = 2 x \cos^{2} x - x^{2} \sin 2 x$
$f^{'} (\frac{π}{4}) = 2 * \frac{π}{4} * \frac{1}{2} - \frac{π^{2}}{16} * 1 = \frac{π}{4} - \frac{π^{2}}{16}$
Apply results in (1)
$(y - \frac{π^{2}}{16}) = (\frac{π}{4} - \frac{π^{2}}{16}) (x - \frac{π}{4})$ is the tangent line equation requested

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Didn't find what you were looking for?