Question-46552

Question Number 46552 by peter frank last updated on 28/Oct/18

Commented by MJS last updated on 28/Oct/18

b) is not clear . what does this mean “ if (it ?)

is parallel to y = 2 x + 3 at {(\begin{matrix} 0 \\ 1 \end{matrix})}^{″} ? if (\begin{matrix} 0 \\ 1 \end{matrix}) is a point

on the curve (\begin{matrix} 0 \\ 4 \end{matrix}) cannot be or vice versa .

please check this

Commented by peter frank last updated on 28/Oct/18

yes sir! definitely problem is not clear

Answered by MJS last updated on 28/Oct/18

f (x) = x^{3} - 3 x^{2} + x + 4

in turning points f^{″} (x) = 0

polynomes of 3^{rd} degree have 1 turning point

f^{″} (x) = 6 x - 6

\Rightarrow turning point T = (\begin{matrix} 1 \\ 3 \end{matrix})

checking the tangent in this point

f^{'} (x) = 3 x^{2} - 6 x + 1

f^{'} (1) = - 2 \Rightarrow tangent decreasing \Rightarrow

\Rightarrow curvature negative (clockwise) for x < 1

curvature positive (counterclockwise) for x > 1

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