A curve has the equation $y = \frac{3}{\sqrt{x}} + x$ and has a turning point at point $P$. Find

Question

A curve has the equation $y = \frac{3}{\sqrt{x}} + x$ and has a turning point at point $P$. Find the coordinates of $P$. Determine the nature of the turning point. Find the equations of tangents to the curve at $x = 1$ and $x = 9$, respectively.

Accepted Answer

(i) $P\left(\left(\dfrac32\right)^{2/3},3\left(\dfrac32\right)^{2/3}\right)$ (ii) Minimum point (iii) $y=-\dfrac12x+\dfrac92$ and $y=\dfrac{17}{18}x+\dfrac32$

Differentiation - Tangents and Normals at a Point

Differentiation - Tangents and Normals at a Point

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