Question

The slope of the tangent to the curve y = 3x2 - 2x +5a the point (1,6)is

Answer 1

SOLUTION

TO DETERMINE

The slope of the tangent to the curve y = 3x² - 2x + 5 at the point (1,6)

EVALUATION

Here the given equation of the curve is

y = 3x² - 2x + 5

Differentiating both sides with respect to x we get

$\displaystyle\sf{ \frac{dy}{dx} = \frac{d}{dx}(3 {x}^{2} - 2x + 5)}$

$\displaystyle\sf{ \implies \frac{dy}{dx} = 3 \frac{d}{dx}( {x}^{2}) - 2 \frac{d}{dx}( x) + \frac{d}{dx}(5)}$

$\displaystyle\sf{ \implies \frac{dy}{dx} = 6x \: - 2 }$

Now

$\displaystyle\sf{ \frac{dy}{dx} \bigg| _{(1,6)} = (6 \times 1) \: - 2 }$

$\displaystyle\sf{ \implies \: \frac{dy}{dx} \bigg| _{(1,6)} =6 \: - 2 }$

$\displaystyle\sf{ \implies \: \frac{dy}{dx} \bigg| _{(1,6)} =4}$

Hence the required slope of the tangent to the curve y = 3x² - 2x + 5 at the point (1,6) is 4

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