Find the values of x given that 30. y = 2x

Find the values of x given that 30. $y = 2x - 3x^{-1}$ and $frac{dy}{dx} = 14$ 31. $y = x^{frac{2}{3}} - x^{frac{1}{3}}$ and $frac{dy}{dx} = frac{1}{4}$ 32. $y = 3x^2 + 4x^{-1}$ and $frac{dy}{dx} = 11$

Transcript

00:01 Hello, i have a question in this way to find the value of y equal to 2x minus 3 x is 1 minus 1 and d by d x is 14.

00:17 So differentiating this with respect to x will be 2 plus 3 by x squared and this is being given at 14.

00:26 So 3 by x square will be equal to 12 x squared is 1 by 4.

00:33 So x is plus minus 1 by 2.

00:40 These are two values for this.

00:43 31 number question.

00:46 Y equal to x rate to power 2 by 3 minus x to power 1 by 3.

00:51 D .y by dx is 1 by 4.

00:57 We'll be differentiating this with respect to x.

01:01 D .y by dx is 2 by 3, x raised to the power minus 1 by 3.

01:08 Minus 1 by 3 x x raised to the power minus 2 by 3 this is 1 by 4 multiplying both sides by 3 2 x raised to the power minus 1 by 3 minus 2 by 2 by 3 equal to 3 by 4 if we assume x raised to the power minus 1 by 3 equal to y question will become 2 y minus y squared equal to 3 by 4 8y minus 4 y square will be equal to 3 4 y square minus 8 y minus 3 plus 3 should be equal to 0 okay so 4 y square minus 6 y minus 2y plus 3 should be equal to 0 take 2 y as common y minus 3 minus 1 2 y minus 3 equal to 0 so 2y minus 3 into 2y minus 1 should be equal to 0 so y will be equal to 3 by 2 from here and y equal to 1 by 2 from here and we had assumed y to be equal to x -rays to the power minus 1 by 3 this is 3 by 2 so cubing x to the power minus 1 will be equal to 27 by 8.

03:05 X will be equal to 8 by 27...

Question

Find the values of x given that 30. $y = 2x - 3x^{-1}$ and $frac{dy}{dx} = 14$ 31. $y = x^{frac{2}{3}} - x^{frac{1}{3}}$ and $frac{dy}{dx} = frac{1}{4}$ 32. $y = 3x^2 + 4x^{-1}$ and $frac{dy}{dx} = 11$

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