Interactive practice questions
A potato farmer finds that the yield (in kg) per square metre when spacing his plants between $0.5$0.5 m and $3.0$3.0 m can be approximated by the following equation:
$y=-\frac{x^2}{4}+\frac{7x}{20}$y=−x24+7x20
Find $\frac{dy}{dx}$dydx.
For what value of $x$x is $\frac{dy}{dx}$dydx equal to $0$0?
What is the maximum possible yield?
Round your answer to two decimal places.
A parabolic satellite dish is pointing straight up. Along a cross-section that passes through the centre of the dish, the height above ground (in metres) is given by the following equation:
$y=\frac{1}{100}\left(x^2-100x\right)+50$y=1100(x2−100x)+50
A function $f:\left[-7,5\right]\to\mathbb{R}$f:[−7,5]→ℝ is given by $f\left(x\right)=-6x^2-12x+90$f(x)=−6x2−12x+90.
A function $f:\left[3,8\right]\to\mathbb{R}$f:[3,8]→ℝ is given by $f\left(x\right)=2x^2-2x-24$f(x)=2x2−2x−24.