First check if (5,0) is on the line:
f(x)= (2x2 + 5)(x3 − 25x)
f(5)= (50+5)(125-125)=0 indeed.
Slope of the tangent line at (5,0) is the value of f'(x) at (5,0), namely f'(5).
So let's find f'(x).
We can find f'(x) as a product, or as an expanded polynomial. I choose the latter:
y = (2x2 + 5)(x3 − 25x)
Differentiate term by term:
= slope of tangent at (5,0)
instantaneous rate of change of the function is precisely f'(x)=dy/dx.
So the answer is the same as in a.
Algebra - If the sides perpendicular to the wall have length x feet, which of ...
calculus - Consider the function f(x)=4x3+2x2+5, and let c be a number in the ...
Math - Consider the following 2x2 system of linear equations, x + y = 3 x + (a^2...
Math: Please check my answers - 1. What is the degree of the monomial 3x2y3? 2 3...
Algebra - A gardener has 60 feet of fencing with which to enclose a garden ...
multivariable calculus - Consider the surface given by the equation: 2x2 - 3z2...
algerba 1 - Solve by graphing 1. 2x2-7x+5=0 2. 2x2+x-6=0
math - graph y=x2,y=2x2 and y=1/2x2 on the same
mathematics - Write all of the following statement(s) that apply to the ...
$$college algebra$$ - Consider g(x) = -2x2 + 36x - 142 for x > 9. Find g-1(12...