Question

find the equation of tangent to the curve x^2-x^4 at ( 1,0)​

Answer 1

Answer:

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Answer 2

Answer:

★Correct Question★

Find the equation of tangent to the curve

$\bf \: y = {x}^{2} - {x}^{4} \: at \: (1 , 0)$

★Answer★

★Given :-

$\bf \:Equation \: of \: curve : y = {x}^{2} - {x}^{4}$

★To find :-

• Equation of tangent at (1, 0).

★Method :-

$\bf \:To \: find \: the \: equation \: of \: tangent, \: we \: need \:$

$\bf 1.\:Slope \: of \: tangent \: (m)$

$\bf 2.\:Point \: (x_1, y_1) \: at \: which \: tangent \: touches \: the \: curve$

$\bf \:Equation \: of \: tangent \: is$

$\bf \:y - y_1 = m(x - x_1)$

★Solution:-

$\bf \:y = {x}^{2} - {x}^{4}$

$\bf \:Differentiate \: w. r. t. \: x$

$\bf\implies \:\dfrac{dy}{dx} = \dfrac{d}{dx} ({x}^{2} - {x}^{4})$

$\bf\implies \:\dfrac{dy}{dx} =\dfrac{d}{dx} {x}^{2} - \dfrac{d}{dx} {x}^{4}$

$\bf\implies \:\dfrac{dy}{dx} =2x - {4x}^{3}$

So, slope of tangent, m is given by

${\red\bigstar\: { \boxed{\large{\bold\red{Slope_{(tangent)}(m)\: = \: \: {\dfrac{dy}{dx} _{(point \: (1 , 0))}}}}}}} \:★$

$\bf\implies m = 2 \times 1 - 4 \times 1$

$\bf\implies \:m = - 2$

Now, equation of tangent is given by

Now, equation of tangent is given by $\bf \:y - y_1 = m(x - x_1)$

$\bf \:Put \: the \: values \: of \: x_1 = 1, y_1 = 0 \: and \: m = - 2, \: we \: get$

$\bf\implies \:y - 0 = - 2(x - 1)$

$\bf\implies \:y = - 2x + 2$

$\bf\implies \:Equation \: of \: tangent \:is \: y = - 2x + 2$

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