Can someone please explain to me what this question is asking and how I should go about solving it: Of all the lines tangent to the curve f(x)=6/(x^2+3) find the x-coordinate of the tangent lines of minimum and maximum slope?
Answers
Answer:
Step-by-step explanation:
Find the derivative of this function.
The derivative would represent the gradient of the tangent at any x value.
The question asks to find the maximum and minimum value of the tangent.
To find this, you have to differentiate the derivative (i.e. find the second derivative of the initial function).
Now let this second derivative be equal to zero to find the maximum and minimum value of the tangents itself. You will get two values of x. These will be your answer.
(To check, put these values of x in the first derivative equation which will give you two values of gradients. One will be positive (maximum gradient) and other will be negative (minimum gradient)
Remember: Don't think that minimum gradient would be zero; gradient can be negative!!)