x = 6
h(x) = (x-1/2 + 5x)(1 - x-1)
What is the question? Are you just supposed to calculate h(6)?
Is your h-1/2 supposed to be h^(-1/2) = 1/sqrt(h) ?
Is the x-1 actually 1/x ?
I looks like all you have to do is plug in 6 for x and do the calculation. That is not calculus.
Im sorry ... it is a derivative question... it says to use the power rule
To evaluate the expression h(x), you need to substitute the value of x into the given expression and simplify it step by step. Let's break down the process:
Step 1: Substitute the value of x into the expression.
h(x) = (x-1/2 + 5x)(1 - x-1)
h(6) = (6 - 1/2 + 5(6))(1 - 6-1)
Step 2: Simplify the numerator.
h(6) = (6 - 1/2 + 30)(1 - 1/6)
Step 3: Perform the calculations within the brackets.
h(6) = (5.5 + 30)(1 - 1/6)
h(6) = (35.5)(1 - 1/6)
Step 4: Simplify the denominator.
h(6) = (35.5)(5/6)
Step 5: Multiply the numerator by the denominator.
h(6) = (35.5 * 5) / 6
h(6) = 177.5 / 6
Step 6: Divide the numerator by the denominator.
h(6) = 29.58 (rounded to two decimal places)
Therefore, h(6) is approximately equal to 29.58.