The variables $x$ and $y$ are connected by the equation $y = x^3 - 3x^2 - 1$. The table below

Question

The variables $x$ and $y$ are connected by the equation $y = x^3 - 3x^2 - 1$. The table below shows some corresponding values of $x$ and $y$. $x$$-2$$-1$$0$$1$$2$$3$$4$ $y$$-21$$-5$$-1$$-3$$a$$-1$$15$ Calculate the value of $a$. Taking $2$ cm to represent $1$ unit on the $x$-axis and $2$ cm to represent $5$ units on the $y$-axis, draw the graph of $y = x^3 - 3x^2 - 1$ for the range of $-2 \leq x \leq 4$. Using your graph, find the value of $x$ when $y = 10$. Using your graph, solve the equation $x^3 - 3x^2 - 2 = 0$, $x^3 - 3x^2 - 2x + 2 = 0$. By drawing a tangent, find the gradient of the curve where $x = 2.5$.

Accepted Answer

(a) $-5$. (c) $3.77$. (d)(i) $3.20$; (ii) $-1,0.59,3.41$. (e) About $3.75$.

Functions and Graphs - Estimating Gradients from Tangents

Functions and Graphs - Estimating Gradients from Tangents

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