A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

To find the gradient of any curve, we take the derivative. So in this case, we need to take dy/dx. We do this by multiplying the term by the power on x, and then lowering the power by one. For example, for the first term, x4, the power is four, so we multiply x4 by four, and the power becomes three, so we have 4x3. We repeat this for all of the terms individually to get dy/dx = 4x-16x +60. 

That gives us the gradient at any point. To get the gradient at x = 6 we need to substitute the value in to the new equation, so we get dy/dx = 4 * 63 - 16 * 6 + 60 = 828

Elizabeth H. A Level Chemistry tutor, GCSE Chemistry tutor, A Level P...

10 months ago

Answered by Elizabeth, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Caitlin R.

Degree: Mathematical Sciences (Bachelors) - Bath University

Subjects offered:Maths


“Hi I'm Caitlin, a first year Maths undergraduate. I am an experienced and patient Maths tutor who achieved A*A*A at A Level”

£26 /hr

Joe C.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“I'm a third year student at Bristol University studying a Masters Degree in Mathematics. I try to make my tutorials engaging, and tailor them to your individual needs so that we are working towards the grade you aspire to achieve! I'v...”

£20 /hr

George B.

Degree: Physics with Industrial experience (Masters) - Bristol University

Subjects offered:Maths, Physics+ 1 more

-Personal Statements-

“I'm a Physics student at the University of Bristol. My passion is Physics and Maths. I love to help people understand what they previously found hard. ”

About the author

£22 /hr

Elizabeth H.

Degree: Natural Science (Masters) - Durham University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics

“Hi! I'm a Natural Sciences student at Durham University studying Physics and Chemistry. I love learning science and applying it to the real world as well as exam and homework questions, and would love to help you do the same!I tutore...”

You may also like...

Other A Level Maths questions

Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.

Find the derivative of the following expression: y=x^3+2x^2+6x+5.

How do i differentiate the equation y = x^2 + 6x + 2 with respect to x.

How do I multiply complex numbers?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss