The variables $x$ and $y$ are connected by the equation $y = 3x^2 + \frac{5}{x}$. Some corresp

Question

The variables $x$ and $y$ are connected by the equation $y = 3x^2 + \frac{5}{x}$. Some corresponding values of $x$ and $y$ are given in the following table. $x$$0.4$$0.6$$0.8$$1$$1.2$$1.4$ $y$$12.98$$9.41$$8.17$$8$$8.49$$p$ Find the value of $p$. Using a scale of $1$ cm to $0.1$ unit, draw a horizontal $x$-axis for $0 \le x \le 1.6$. Using a scale of $1$ cm to $1$ unit, draw a vertical $y$-axis for $0 \le y \le 14$. On your axes, plot the points given in the table and join them with a smooth curve. Use your graph to find the least value of $y$. Use your graph to find two solutions of $3x^2 + \frac{5}{x} = 9$ in the range $0 \le x \le 1.6$. By drawing a tangent, find the gradient of the curve at the point $(0.8, 8.17)$. On the same axes, draw the graph of $y = 2x + 7$ for $0 \le x \le 1.6$. Write down $x$-coordinate of the point where the two graphs intersect. This value of $x$ is a solution of the equation $3x^3 + Ax^2 + Bx + C = 0$. Find the value of $A$, $B$ and $C$.

Accepted Answer

(a) $9.45$ (c) $8$ (d) $0.65,1.32$

Functions and Graphs - Graphical Solution and Gradient of the Curve at a Point

Functions and Graphs - Graphical Solution and Gradient of the Curve at a Point