Find the slope of the tangent to given curve at the indicated point as instructed:
y =\( {x }^{4 } \) - 6\( { x}^{ 3} \) + 13\( { x}^{ 2} \) + 10x + 5 at (0,5) :
Answer & explanation
Correct answer: option 1
Slope of tangent is
$\frac{dy}{dx}=4x^3-18x^2+26x+10$
at (0, 5)
$\frac{dy}{dx}=10$
Equation of tangent is
$y - 5 = 10(x-0)$
$y=10x+5$