Questions: (f(x+h)-f(x))/h

(f(x+h)-f(x))/h
Transcript text: \[ \frac{f(x+h)-f(x)}{h}= \]
failed

Solution

failed
failed

Solution Steps

Step 1: Substitute \( f(x+h) \) and \( f(x) \) into the expression

Given \( f(x) = -5x^2 \), substitute \( f(x+h) \) and \( f(x) \) into the expression \( \frac{f(x+h) - f(x)}{h} \): \[ f(x+h) = -5(x+h)^2 \] \[ f(x) = -5x^2 \] Thus: \[ \frac{f(x+h) - f(x)}{h} = \frac{-5(x+h)^2 - (-5x^2)}{h} \]

Step 2: Expand \( (x+h)^2 \) and simplify the numerator

Expand \( (x+h)^2 \): \[ (x+h)^2 = x^2 + 2xh + h^2 \] Substitute this back into the expression: \[ \frac{-5(x^2 + 2xh + h^2) + 5x^2}{h} \] Simplify the numerator: \[ -5x^2 - 10xh - 5h^2 + 5x^2 = -10xh - 5h^2 \]

Step 3: Factor out \( h \) and simplify

Factor \( h \) out of the numerator: \[ \frac{-10xh - 5h^2}{h} = \frac{h(-10x - 5h)}{h} \] Cancel \( h \) in the numerator and denominator: \[ -10x - 5h \]

Step 4: Final expression

The simplified expression is: \[ -10x - 5h \]

Final Answer

\(\boxed{-10x - 5h}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Surgery to the heart damages the cardioaccelerator nerve. What happens to the patient's blood pressure and cardiac output upon standing rapidly when blood is momentarily pooled away from the head and neck? a.) Both cardiac output and blood pressure will increase b.) Both cardiac output and blood pressure will decrease c.) Cardiac output will decrease, while blood pressure will increase d) Cardiac output will increase, while blood pressure will decrease
failedAnswered
Rob It seems to me this is a very flat organizational structure, William Lopez. With my limited knowledge of this business discipline, I thought a flat structure is the best structure for an organization of our size, correct? you anom sabelina. I wouldn't necessarily call this a flat structure when you consider that there are seven departments and over 100 employees. I am not certain that these survey results are related to organizational design. Yes, I agree the structure is very flat with everyone reporting directly to you and Isabella. This is the best structure to empower employees and create autonomy. Consequently, the survey results don't make much sense.
failedAnswered
A model rocket is launched with an initial upward velocity of 40 m/s. The rocket's height h (in meters) after t seconds is given by the following: h = 40t - 5t^2 Find all values of t for which the rocket's height is 15 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.) t = [] seconds
failedAnswered
Which term is defined as discrimination against an ethnic group that is assumed to have a biological basis? prejudice racism ethnocide genocide stereotyping Some statuses aren't mutually exclusive; they may be
failedAnswered
Translate to an equation and solve. 40 is 80% of what? 40 is 80% of (Simplify your answer. Type an integer or a decimal.)