The curve is $y=x^3-4x$, for $-2.5\leq x\leq2.5$. Use the supplied axes. In this question,

Question

The curve is $y=x^3-4x$, for $-2.5\leq x\leq2.5$. Use the supplied axes. In this question, obtain roots and the gradient graphically; do not use differentiation or an equation solver. $x$-2.5-2-1.5-1-0.500.511.522.5 $y$-5.625031.8750-1.875-3-2.6250 Complete the two missing entries in the table.[2] Plot the points and draw a smooth curve through them.[3] On the same axes draw a suitable straight line and use it to solve $x^3-5x+1=0$, giving your three estimates to 1 decimal place.[2] Draw a tangent to the curve at $x=1$. Use a large gradient triangle to estimate its gradient.[2] Explain why a graphical answer is an estimate rather than an exact value.[1]

Accepted Answer

(a) 2.625,5.625. (b) Smooth cubic. (c) $y=x-1$; $x\approx-2.3,0.2,2.1$. (d) About −1. (e) Finite drawing/read-off precision.

A curve and graphical solutions

A curve and graphical solutions

Solution:

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