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Equation of Tangent at a Point (x,y) in Terms of f'(x)

Prove that th...

Question

Prove that the tangent drawn at any point to the curve $f (x) = x^{5} + 3 x^{3} + 4 x + 8$ would make an acute angle with $x$ -axis.

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Solution

$f (x) = x^{5} + 3 x^{3} + 4 x + 8$
$f (x) = 5 x^{4} + 9 x^{2} + y$
for all valume of x the f(x)fx
in increasing
$t a n θ = 5 x^{4} + 9 x^{2} + y$
The angle will always between
0 to 90 $^{\circ}$
so the angle in acute angle for all value.

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