Recently I came across this question that my teacher asks my whole class to do as homework :
Find the coordinates of the points on the curve y = x(x - 2)^2 - 3 at which the gradient is 7.
To provide a background information, my teacher has never taught my class this kind of question before as she teaches my class only the basic rules of differentiation by far and has never taught us how to solve this type of question.
Any kind soul can explain this question to me? Your help will be greatly appreciated. Thanks.
So basically differentiation has various uses, and one of them is finding the gradient of the curve. When u differentiate y=x (x-2)^2-3 u will get the equation of the gradient. (Hint* use product rule and chain rule) After that let dy/dx =7 since dy/dx is the gradient. Solve for x and later find y
Hmmm... my teacher haven't touched on chain or product rule yet. She only introduced the derivative, power rule, constant multiple rule and sum/difference rule. So what you meant was to differentiate the equation and solve simultaneous equations to get the required coordinates? The answer key shows that there are 2 different full coordinates to find but it never showed the step-by-step soultions.
if no learn product rule, u can expand the bracket. multiply in the x. then differentiate
dy/dx = 7
shift all to one side
solve the quadratic eqn
u shd have 2 x answers
find y for each
there u have. 2 coords.
Ohhh now I understand. Thank you so much for those who helped :)