F(x) = x^5 - x^3 + x
f'(x) = 5x^4 - 3x^2 + 1
f(3) = (3)^5 - (3)^3 + 3 = 243 - 27 + 3 = 219
f'(3) = 5(3)^4 - 3(3)^2 + 1 = 5(81) - 3(9) + 1 = 405 - 27 + 1 = 379
Let the required equation of the tangent line be
y = mx + c; where y = 219, m = 379, x = 3
219 = 379(3) + c = 1,137
c = 219 - 1,137 = -918
Therefore, required equation is
y = 379x - 918
Answer:
Step-by-step explanation:
The mean is found by adding the time it takes Greg each day and then diving by the number of days: 27+25+32=84.
84/3=28 min
it takes Greg 32 min on the third day
Answer:
$50,281.04
Step-by-step explanation:
5 years is equivalent to (5 × 12) = 60 months
Now, the first payment $670 is compounded for 60 months at the rate of
% monthly interest.
So, it will become
.
Similarly the second payment of $670 will become 
Therefore, in this way after 60 months i.e. 5 years the total sum will be
= 
= ![670[1 + (1.0067) + (1.0067)^{2} + (1.0067)^{3} + ....... + (1.0067)^{59} + (1.0067)^{60} ]](https://tex.z-dn.net/?f=670%5B1%20%2B%20%281.0067%29%20%2B%20%281.0067%29%5E%7B2%7D%20%2B%20%281.0067%29%5E%7B3%7D%20%2B%20.......%20%2B%20%281.0067%29%5E%7B59%7D%20%2B%20%281.0067%29%5E%7B60%7D%20%5D)
= ![670[1 \times \frac{(1.0067)^{61} - 1 }{1.0067 - 1} ]](https://tex.z-dn.net/?f=670%5B1%20%5Ctimes%20%5Cfrac%7B%281.0067%29%5E%7B61%7D%20-%201%20%7D%7B1.0067%20-%201%7D%20%5D)
= $50,281.04 (Answer)
{Since, the sum of the G.P. series
}