Question

find the equation and notmal to the curve y=x^4_6x^3+13x^2_10x+5 at(0,5)​

Answer 1

Given, equation of curve is

$x^{4} -6x^{3} + 13x^{2} - 10x +5$

On differentiating both sides w.r.t. x, we get

$dy/dx = 4x^{3} - 18x^{2} - 26x -10$

Slope of a tangent at point $(1,0)$  is

$m = [dy/dx](...x=1) =4-18+26-10=2$

∴ Equation of tangent at point $(1,0)$ having slope 2 is

$y-0=2(x-1)\\y=2x-2$

or

Hence, required equation of tangent is $2x-y=2$

$Thanks$

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