Hi there. For g(x)=4x² -3x +1 Find the rate of change for: A) x=1 and x=3 B) (x, f(x)) and (x+h, f(x+h) I dont know how and would appreciate an explanation. Thanks so much.
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Perhaps you just need the definition for average rate of change? Between x=a and x=b, the average rate of change is (change in g(x) divided by the change in x): For example, average rate of change between x=0 and x=1 is
So, for the first part it would be: (4-3+1)-(36-9+1)/1-3 Which becomes 12 Also, I am confused about B). So for I got it to f(x+h)-f(x)/(x+h)-x Then I simplified it to 3(x+h)²-3x²/h Did I do it correctly?
Originally Posted by theridon So, for the first part it would be: (4-3+1)-(36-9+1)/1-3 Which becomes 12 Also, I am confused about B). So for I got it to [f(x+h)-f(x)]/(x+h)-x brackets are important! Then I simplified it to 3(x+h)²-3x²/h - where did that 3 come from? Did I do it correctly? See red comments
Sorry about the brackets, thats what I meant. I think you plug it into 4x² -3x +1, correct? This is how I got there: 1. [f(x+h)-f(x)]/(x+h)-x 2. [[3(x+h)²+1]-(3x²+1)]/h 2. 3(x+h)²-3x²/h
Originally Posted by theridon Sorry about the brackets, thats what I meant. I think you plug it into 4x² -3x +1, correct? This is how I got there: 1. [f(x+h)-f(x)]/(x+h)-x 2. [[3(x+h)²+1]-(3x²+1)]/h 2. 3(x+h)²-3x²/h yes, but that's not what you did. first of all, is ??? you called it . if so, the numerator should be ...
Oh I missed the first part. So then it would become: [4x²+8xh-3x-3h+1-4x²+3x-1]/h (4h²+8hx)/h 4h+8x Which simplifies to 4(h+2x) I believe its correct
Originally Posted by theridon Oh I missed the first part. So then it would become: [4x²+8xh-3x-3h+1-4x²+3x-1]/h (4h²+8hx)/h 4h+8x Which simplifies to 4(h+2x) I believe its correct numerator again ...
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