Differentiation

New Zealand

Level 7 - NCEA Level 2

Find the gradient of $f\left(x\right)=x^5-3x^4$`f`(`x`)=`x`5−3`x`4 at the point $\left(3,0\right)$(3,0).

Denote this gradient by $f'\left(3\right)$`f`′(3).

Easy

1min

Consider the curve given by the function $f\left(x\right)=-\frac{27}{x^2}$`f`(`x`)=−27`x`2.

Easy

2min

Find the gradient of $f\left(x\right)=\frac{11}{x}+\frac{10}{x^2}$`f`(`x`)=11`x`+10`x`2 at the point $\left(4,\frac{27}{8}\right)$(4,278).

Denote this gradient by $f'\left(4\right)$`f`′(4).

Easy

2min

Find the gradient of $f\left(x\right)=\frac{6}{\sqrt{x}}$`f`(`x`)=6√`x` at the point $\left(25,\frac{6}{5}\right)$(25,65).

Denote this gradient by $f'\left(25\right)$`f`′(25).

Easy

2min

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