Jodie is attempting to use differentiation from first principles to prove that the gradient of
$y = ext{sin} x$ is zero when $x = \frac{\pi}{2}$ - AQA - A-Level Maths Pure - Question 11 - 2019 - Paper 1
Question 11
Jodie is attempting to use differentiation from first principles to prove that the gradient of
$y = ext{sin} x$ is zero when $x = \frac{\pi}{2}$.
Jodie’s teacher t... show full transcript
Worked Solution & Example Answer:Jodie is attempting to use differentiation from first principles to prove that the gradient of
$y = ext{sin} x$ is zero when $x = \frac{\pi}{2}$ - AQA - A-Level Maths Pure - Question 11 - 2019 - Paper 1
Step 1
For gradient of curve at A,
let $h = 0$ then
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Answer
As we move towards the limit where h approaches 0, we simplify the terms.
By the definition of the derivative, we know that:
limh→0hsin(h)=1
Thus, substituting in the values as h approaches 0 gives us:
cos(h)→1 as h→0.
hsin(h)−sin(0)→1
Therefore:
The gradient of the curve at A now becomes:
sin(2π)⋅0+cos(2π)⋅1=1⋅0+0⋅1=0.
