Search topics

Search
1 of 8 0-day streak

Gradient of a tangent from first principles

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
quadratic, quotient, positive leading coefficientquadratic, derivative-rule, positive leading coefficientquadratic, gradient, positive leading coefficientquadratic, quotient-and-gradient, positive leading coefficientcubic, quotient, positive leading coefficientcubic, derivative-rule, positive leading coefficientcubic, gradient, positive leading coefficientcubic, quotient-and-gradient, positive leading coefficientNOWMix of allRecommended
Question 1 of 8

No calculator

Consider the polynomial function given by the rule below

\[q(x)=-x^2 - x + 4\]

The target value is shown below. Use the limit definition of the derivative

\[x=-3\]

The difference quotient is

\[\frac{q(x+h)-q(x)}{h}\]
(a)1 mark

Use first principles to obtain the requested expression, then find the gradient at the target value. Select the simplified difference quotient

(b)1 mark

Find the exact gradient at the target value