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Answer: Linear model and H'(t) = 9 units.
Step-by-step explanation:
Since we have given that
In 2000, amount spent = $100 billions
In 2010, amount spent = $190 billions.
So, rate of increase would be
So, linear model for H(t) would be
So, H'(t) would be 9.
Hence, linear model and H'(t) = 9 units.
Answer:
Step-by-step explanation:
The slope of the tangent to a curve is the derivative of the curve. We need to find the derivative of the function and then evaluate the derivative at that given x value. The derivative is found using the product rule:
Let's call 3x our f(x) and sin(x) our g(x). Filling in the formula for the derivative using the product rule looks like this:
That gives us the derivative, which is the slope formula that can be used at ANY x value anywhere on the curve to find the slope of the line tangent to the curve at that x value. If we want to find the slope of the tangent line to the curve at x = pi/2, we evaluate the slope formula at x = pi/2 (remember that y' is the same exact thing as the slope):
From the unit circle (or experience, since you're in advaced math), we know that the cosine of pi/2 is 0 and that the sin of pi/2 = 1:
simplifies to
y' (slope) = 3
That means that the slope of the line tangent to the curve at the point x = pi/2 is 3.