Question

find the point on the curve y=7x-3xsquare where the inclination of the tangent is 45

Answer 1

Hope u studied derivatives.

Answer 2

The required point is (1,4)

Given :

The equation of the curve y = 7x - 3x²

To find :

The point on the curve y = 7x - 3x² where the inclination of the tangent is 45°

Solution :

Step 1 of 3 :

Write down the equation of the curve

The given equation of the curve is

y = 7x - 3x² - - - - - - (1)

Step 2 of 3 :

Find slope of the tangent at any point on the curve

$\displaystyle \sf{ y = 7x - 3{x}^{2} }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx} =\frac{d}{dx} (7x - 3 {x}^{2} ) }$

$\displaystyle \sf{ \implies \frac{dy}{dx} = 7 - 6x}$

So slope of the tangent at point (x, y) on the curve is given by

m = 7 - 6x

Step 3 of 3 :

Find the required point

Let the required point is (x, y)

Since the inclination of the tangent is 45°

∴ m = tan 45°

$\displaystyle \sf{ \implies 7 - 6x = 1}$

$\displaystyle \sf{ \implies \: - 6x = - 6}$

$\displaystyle \sf{ \implies x = 1}$

Now for x = 1 we have from Equation 1

y = 7 × 1 - 3 × 1²

⇒ y = 7 - 3

⇒ y = 4

Hence the required point is (1,4)

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