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Grade 12 calculus help!?

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Determine the slope of the tangent to each curve at the given value of x. a) y = x^3, x = -2 b) y = √5x - 1, x = 2 For question b) the entire thing 5x - 1 is under the square root c) y = 1 / (x+2), x = 3 I tried using the tangent formula, but it's not working... I'm not getting the correct... 

asked Feb 13, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1 :

(a)

The function is image.

The slope of the tangent line is equal to the derivative of the function.

image

Differentiate the function with respect to

image

Apply power rule of derivatives : image.

image.

At image, image.

The slope of the tangent to the curve image at image is 12.

Step 2 :

(b)

The function is image.

The slope of the tangent line is equal of the derivative of the function.

image

Differentiate the function with respect to

image

image

Apply power rule of derivatives : image.

image

At image,

image

The slope of the tangent to the curve image at image is image.

answered Feb 14, 2015 by lilly Expert

Contd...

Step 3 :

(c)

The function is image.

The slope of the tangent line is equal of the derivative of the function.

image

image

Differentiate the function with respect to

image

Apply power rule of derivatives : image.

image

At image, image.

The slope of the tangent to the curve image at image is image.

Solution :

(a) The slope of the tangent to the curve image at image is 12.

(b) The slope of the tangent to the curve image at image is image.

(c) The slope of the tangent to the curve image at image is image.

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