Grade 12 calculus help!?

Question

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... 

Answer 1

Step 1 :

(a)

The function is .

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

Differentiate the function with respect to . 

Apply power rule of derivatives : .

.

At , .

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

Step 2 :

(b)

The function is .

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

Differentiate the function with respect to . 

Apply power rule of derivatives : .

At ,

The slope of the tangent to the curve at is .

Comments

Contd...

Step 3 :

(c)

The function is .

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

Differentiate the function with respect to . 

Apply power rule of derivatives : .

At , .

The slope of the tangent to the curve at is .

Solution :

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

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

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