Photo AI

Find an equation of the tangent to the curve $y = (x - 2)^4$ at the point where $x = 0$ - AQA - A-Level Maths Pure - Question 5 - 2022 - Paper 1

Question 5

Find an equation of the tangent to the curve $y = (x - 2)^4$ at the point where $x = 0$

Worked Solution & Example Answer:Find an equation of the tangent to the curve $y = (x - 2)^4$ at the point where $x = 0$ - AQA - A-Level Maths Pure - Question 5 - 2022 - Paper 1

Step 1

96%

114 rated

Answer

To find the equation of the tangent, we first need to differentiate the function. The function is given by:

$y = (x - 2)^4$

Using the chain rule, we differentiate:

$\frac{dy}{dx} = 4(x - 2)^3$

Step 2

99%

104 rated

Answer

Next, we substitute $x = 0$ into the derivative to find the slope of the tangent line:

$\frac{dy}{dx} \bigg|_{x=0} = 4(0 - 2)^3 = 4(-8) = -32$

Step 3

96%

101 rated

Answer

Now, we need the point on the curve at $x = 0$ to complete the equation of the tangent line. By substituting $x = 0$ into the original function:

$y = (0 - 2)^4 = 16$

Thus, the point is $(0, 16)$ with a slope of $-32$ . Using point-slope form, the equation of the tangent line is:

$y - 16 = -32(x - 0)$

Simplifying this, we have:

$y = -32x + 16$

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;