The exponential function f, whose graph is given below, can be written as
1 answer:
Answer:
f(x) = 2·3^x
Step-by-step explanation:
We have the general equation of exponential functions as
y= a*b^x
We are given that the point (0,2) is on the graph so
when x= 0, y= 2
If we substitute in the general equation we see that
2 = a*b^0, any number to the power 0 is 1
2 = a
We were also given that point (1, 6 ) is on the graph;
If we substitute in our new found equation we see that
y=2·b^x
6 = 2·b^1 , any number to the power 1 is itself and
divide both sides by 2
3 = b
f(x) = 2·3^x
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Your answer It would be y=2x+4
Answer:
The minimum value of f(x) is 2
Step-by-step explanation:
- To find the minimum value of the function f(x), you should find the value of x which has the minimum value of y, so we will use the differentiation to find it
- Differentiate f(x) with respect to x and equate it by 0 to find x, then substitute the value of x in f(x) to find the minimum value of f(x)
∵ f(x) = 2x² - 4x + 4
→ Find f'(x)
∵ f'(x) = 2(2) - 4(1)
+ 0
∴ f'(x) = 4x - 4
→ Equate f'(x) by 0
∵ f'(x) = 0
∴ 4x - 4 = 0
→ Add 4 to both sides
∵ 4x - 4 + 4 = 0 + 4
∴ 4x = 4
→ Divide both sides by 4
∴ x = 1
→ The minimum value is f(1)
∵ f(1) = 2(1)² - 4(1) + 4
∴ f(1) = 2 - 4 + 4
∴ f(1) = 2
∴ The minimum value of f(x) is 2